MAYBE

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict Trs:
  { f(nil()) -> nil()
  , f(.(nil(), y)) -> .(nil(), f(y))
  , f(.(.(x, y), z)) -> f(.(x, .(y, z)))
  , g(nil()) -> nil()
  , g(.(x, nil())) -> .(g(x), nil())
  , g(.(x, .(y, z))) -> g(.(.(x, y), z)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following weak dependency pairs:

Strict DPs:
  { f^#(nil()) -> c_1()
  , f^#(.(nil(), y)) -> c_2(f^#(y))
  , f^#(.(.(x, y), z)) -> c_3(f^#(.(x, .(y, z))))
  , g^#(nil()) -> c_4()
  , g^#(.(x, nil())) -> c_5(g^#(x))
  , g^#(.(x, .(y, z))) -> c_6(g^#(.(.(x, y), z))) }

and mark the set of starting terms.

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { f^#(nil()) -> c_1()
  , f^#(.(nil(), y)) -> c_2(f^#(y))
  , f^#(.(.(x, y), z)) -> c_3(f^#(.(x, .(y, z))))
  , g^#(nil()) -> c_4()
  , g^#(.(x, nil())) -> c_5(g^#(x))
  , g^#(.(x, .(y, z))) -> c_6(g^#(.(.(x, y), z))) }
Strict Trs:
  { f(nil()) -> nil()
  , f(.(nil(), y)) -> .(nil(), f(y))
  , f(.(.(x, y), z)) -> f(.(x, .(y, z)))
  , g(nil()) -> nil()
  , g(.(x, nil())) -> .(g(x), nil())
  , g(.(x, .(y, z))) -> g(.(.(x, y), z)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

No rule is usable, rules are removed from the input problem.

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { f^#(nil()) -> c_1()
  , f^#(.(nil(), y)) -> c_2(f^#(y))
  , f^#(.(.(x, y), z)) -> c_3(f^#(.(x, .(y, z))))
  , g^#(nil()) -> c_4()
  , g^#(.(x, nil())) -> c_5(g^#(x))
  , g^#(.(x, .(y, z))) -> c_6(g^#(.(.(x, y), z))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The weightgap principle applies (using the following constant
growth matrix-interpretation)

The following argument positions are usable:
  Uargs(c_2) = {1}, Uargs(c_3) = {1}, Uargs(c_5) = {1},
  Uargs(c_6) = {1}

TcT has computed following constructor-restricted matrix
interpretation.

        [nil] = [1]         
                            
  [.](x1, x2) = [1] x2 + [0]
                            
    [f^#](x1) = [1] x1 + [0]
                            
        [c_1] = [0]         
                            
    [c_2](x1) = [1] x1 + [2]
                            
    [c_3](x1) = [1] x1 + [1]
                            
    [g^#](x1) = [0]         
                            
        [c_4] = [1]         
                            
    [c_5](x1) = [1] x1 + [2]
                            
    [c_6](x1) = [1] x1 + [1]

This order satisfies following ordering constraints:


Further, it can be verified that all rules not oriented are covered by the weightgap condition.

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { f^#(.(nil(), y)) -> c_2(f^#(y))
  , f^#(.(.(x, y), z)) -> c_3(f^#(.(x, .(y, z))))
  , g^#(nil()) -> c_4()
  , g^#(.(x, nil())) -> c_5(g^#(x))
  , g^#(.(x, .(y, z))) -> c_6(g^#(.(.(x, y), z))) }
Weak DPs: { f^#(nil()) -> c_1() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {3} by applications of
Pre({3}) = {4}. Here rules are labeled as follows:

  DPs:
    { 1: f^#(.(nil(), y)) -> c_2(f^#(y))
    , 2: f^#(.(.(x, y), z)) -> c_3(f^#(.(x, .(y, z))))
    , 3: g^#(nil()) -> c_4()
    , 4: g^#(.(x, nil())) -> c_5(g^#(x))
    , 5: g^#(.(x, .(y, z))) -> c_6(g^#(.(.(x, y), z)))
    , 6: f^#(nil()) -> c_1() }

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { f^#(.(nil(), y)) -> c_2(f^#(y))
  , f^#(.(.(x, y), z)) -> c_3(f^#(.(x, .(y, z))))
  , g^#(.(x, nil())) -> c_5(g^#(x))
  , g^#(.(x, .(y, z))) -> c_6(g^#(.(.(x, y), z))) }
Weak DPs:
  { f^#(nil()) -> c_1()
  , g^#(nil()) -> c_4() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The following weak DPs constitute a sub-graph of the DG that is
closed under successors. The DPs are removed.

{ f^#(nil()) -> c_1()
, g^#(nil()) -> c_4() }

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { f^#(.(nil(), y)) -> c_2(f^#(y))
  , f^#(.(.(x, y), z)) -> c_3(f^#(.(x, .(y, z))))
  , g^#(.(x, nil())) -> c_5(g^#(x))
  , g^#(.(x, .(y, z))) -> c_6(g^#(.(.(x, y), z))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..